Nonlinear EI Equation for Slender Composite Columns Bending about the Minor Axis

The moment magnifier method was introduced into design practice to eliminate the need for extensive calculations, based on the solution to a differential equation, for the second-order moments in slender columns. This method is strongly influenced by the effective flexural stiffness (EI), which varies due to the nonlinearity of the concrete stress–strain curve and the cracking along the column length among other factors. The EI equations given in the ACI building code are approximate when compared to the EI values computed from the axial load–bending moment–curvature relationships. This study was undertaken to determine the influence of a full range of variables on EI used for the design of slender, tied, composite columns in which the bending moment was applied about the minor axis of the steel shape encased in concrete, and also to examine the existing ACI EI equations. Approximately 12,000 isolated square composite columns, each with a different combination of specified properties of variables, were simulated and used to generate the stiffness data. The columns studied were subjected to short-term ultimate loads and equal and opposite end moments causing symmetrical single curvature bending. A new nonlinear equation for EI was then developed for use in design of slender composite columns subjected to minor axis bending and is proposed as an alternative to the existing ACI EI equations.